rational root theorem

Answer:

89.44

Step-by-step explanation:

using the Pythagorean Theorem: \(a^{2} +b^{2}=c^{2}\)

\(80^{2} +b^{2} =120^{2} \\6400+b^{2} =14400\\b^{2} = 8000\\b = 40\sqrt{5}\)

120 is the hypotenuse so it would be c in the equation.

To solve, I simplified and isolated the variable. I got the square root of 8000 simplified (but idk how to write that out lol)

This answer is closest to 89.44

*Hope this helped! Have a great day/ night wherever you are! : )*

Answer:

256

Step-by-step explanation:

65% is 208

15% is 48

15% + 65% is 80%

So, just add 48 and 208 together:

48 + 208 = 256

Therefore, 80% of that number is 256.

Answer:

256

Step-by-step explanation:

We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.

The length of AB is 26cm.

What is the perimeter of a triangle?

The perimeter of a triangle is the sum of the lengths of all its sides.

Let's start by using variables to represent the lengths of the sides of the triangle:

AC = x

AB = 2x

BC = (2x - 6)

We know that the perimeter of the triangle is 59cm, so we can write an equation:

AC + AB + BC = 59

Substituting in the expressions we have for each side, we get:

x + 2x + (2x - 6) = 59

Simplifying the equation, we get:

5x - 6 = 59

Adding 6 to both sides, we get:

5x = 65

Dividing both sides by 5, we get:

x = 13

So we know that AC = 13. Using the expression we have for AB, we get:

AB = 2x = 2(13) = 26

Hence, the length of AB is 26cm.

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The probability that at least one of them is operational is 0.999

Probability:

Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.

Given,

The probability a D-Link network server is down is 0.10.

Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.

Let D be an event that a D-Link network server is down.

It is given that the probability that a D-Link network server is down is

=> P(D) = 0.10

The number of independent servers

=> (n) = 3

The probability that none of the servers is working is

=>P(None) = P(D) x P(D) x P(D)

=> P(None) = 0.10 x 0.10 x 0.10

=> P(None) = 0.001

The probability that at least one of them is operational is given as

=> 1 - P(None)

=> 1 - 0.001

=> 0.999

Therefore, the probability that at least one of them is operational is 0.999.

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The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:

First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.

Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.

Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.

Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:

(4/6) * (4/6) = 16/36

To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):

16/36 = 4/9

So, the probability of drawing 2 green balls simultaneously is 4/9.

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Answer:

need help

Step-by-step explanation:

Carla is 1.3 miles away from the home.

Given that, Carla leaves home and walks 40° easy to the north for 1.5 miles, then turns and continues due west for 2 miles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

Here, c=√(1.5²+2²-2×1.5×2 cos40°)

c=√(2.25+4-6×0.7660)

c=√1.654

c=1.28

c=1.3 miles

Therefore, Carla is 1.3 miles away from the home.

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Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

Answer:

Take Action: Take Time to Plan. ...

Take a Break: Get Out of the Office. ...

Take Action: Talk it Out with a Colleague. ...

Take a Break: Get a Full Night's Sleep. ...

Take Action: Work on the Weekends.

Answer:

If your due dates are at least by the end of the week, I recommend doing straight work for 30 minutes, then rewarding yourself. Repeat this for as long as you want but don't do so much that you weren't able to do anything socially for the whole day. If your due dates are already passed or if they are coming up really soon, I recommend putting on whatever music you like to listen to, but nothing to upbeat. Put on some calm music with a rain sound effects video in the background, and just keep working until you kind of dose off from reality and just get in the zone. A long answer, but it really helps.

Forgot to mention; if you ever get stressed out, either do something else to calm down, or use that stress to your advantage and do a ton of work because of it.

The equation to determine Carl's savings after any number of weeks is: Savings = 30 * (number of weeks) + 20.

The pattern in Carl's savings can be observed by looking at the amount of money he saves each week. It increases by $30 every week. Initially, in Week 1, Carl saves $50. Then, in Week 2, he saves $80, which is $30 more than Week 1. This pattern continues, with an additional $30 being saved each week.

To calculate Carl's savings after any number of weeks, we can use the equation: Savings = 30 * (number of weeks) + 20. The term "30 * (number of weeks)" represents the additional amount saved each week, multiplied by the number of weeks. The constant term "+ 20" accounts for the initial $20 that Carl had saved before Week 1.

By substituting the desired number of weeks into the equation, we can determine the total savings. This equation provides a simple and efficient way to calculate Carl's savings after any number of weeks.

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Answer:

Hope this helps!! (x,y)=(6,-5)

Answer:

y=-5

x=6

Step-by-step explanation:

substitute y=4x -29 into the equation x+y=1.

x+ 4x-29 = 1

combine like terms

5x-29=1

add 29 to both sides

5x=30

divide by 5

x=6

plug 6 into x in the original equation

y=4(6) - 29

y=24-29

y= -5

The correct hypothesis statement would be:

H0: μ = 45 (null hypothesis)

H1: μ ≠ 45 (alternative hypothesis)

The null hypothesis (H0) represents the current belief or assumption, and states that the population mean is equal to a specific value, which in this case is 45 minutes. The alternative hypothesis (H1) is the opposite of the null hypothesis, and states that the population mean is not equal to 45 minutes.

This hypothesis statement assumes a two-tailed test, where the researcher is interested in detecting any significant deviation from the hypothesized mean in either direction. This means that the researcher will reject the null hypothesis if the sample mean is either significantly higher or significantly lower than 45 minutes, based on the level of significance chosen for the test.

Option D correctly states the null hypothesis but incorrectly states the alternative hypothesis. Option A correctly states the alternative hypothesis but incorrectly states the null hypothesis. Option C states a one-tailed alternative hypothesis, which is only appropriate if the researcher has a specific direction in mind (e.g., if they expect the average time to be longer than 45 minutes).

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

If you solve this inequality you should get...

\(4<3+4x\\1<4x\\\frac{1}{4} <x\)

So I don't know if you can but the answer is all three because 9, 7, and 1 are all greater than \(\frac{1}{4}\).

The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Answer:37

Step-by-step explanation:

Answer:

r = 37

Step-by-step explanation:

2r = 56+ 18

2r = 74

r = 37

Answer:

f(2) = 0

Step-by-step explanation:

f(2) with t = 2 satisfies the condition t ≠ 8, 10 , then using

f(t) = t² - 3t + 2

f(2) = 2² - 3(2) + 2 = 4 - 6 + 2 = 0

Answer:

3 whole number 21 over 24 ingredients are used.

3 21/24

Step-by-step explanation:

1⅜ + 1 5/6 + ⅔

Step 1

convert it to improper fractions

= 11/8 + 11/6 + 2/3

look for the LCM which is 24

= 33 + 44 + 16/24

= 93/24

= 3 21/24

The solution is available in the attachments. In summary, we learned how to convert a whole fraction into a compound fraction and equalized the denominators to do arithmetic with rational expressions. Good luck.

Answer:

x = 14

Step-by-step explanation:

First, use the distributive property:

-7x + 14 = -84

-7x = -98

x = 14

Answer:

my answer got deleted for no reason so ill add it again with my way of solving it with steps this time.

x=14

Step-by-step explanation:

divide both sides by -7

\(\frac{-7(x-2)}{-7} =\frac{-84}{-7}\)

simplify

\(x-2=12\)

add two to both sides

\(x-2=12\)

    \(+2\)   \(+2\)

simplify

\(x=14\)

hope having another method helps :)

The Vertex, Focus and Directrix of Parabola are ( 1, -7),  (1, 85/12) and y = 434.  

For a parabola y = ax²+bx+c the formulas for Vertex, Focus, and Directrix are given by

Vertex = [ -b/2a, (4ac -b²)/4a ]  

Focus =  [ -b/2a, (4ac -b² +1)/4a ]    

Directrix, y = c -(b² + 1)4a  

Here we have

3x² - 6x +y +10=0    

=> 3x² - 6x +y +10=0    

=> y = - 3x² + 6x - 10  

Compare the given equation with y = ax²+bx+c

=> a = - 3

=> b = 6

=> c = - 10

Vertex = [ -6/2(-3), (4(-3)(-10) -6²)/4(-3) ]

=  [ -6/-6, (120 -36)/-12 ]

= [ 1, -7]

Focus =  [ -b/2a, (4ac -b² +1)/4a ]    

=  [ -6/2(-3), (4(-3)(-10) -6² +1)/4(-3) ]    

=  [ 1, 85/12]

Directrix, y = c -(b² + 1)4a  

=> y = -10 - [ (-6)²+1 ] 4(-3)

=> y = -10 - [ 36 + 1 ] -12

=> y = -10 + 444

=> y =  434

Therefore,

The Vertex, Focus and Directrix of Parabola are ( 1, -7),  (1, 85/12) and y = 434.  

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This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Hey there!

The answer to your question is $240.87

First we need to find how much he earned:

9.75 x 30

292.50

Now, we find the amount of all the deductions:

292.50(0.1 + 0.062 + 0.0145)

51.63

Now, we take this off the total pay:

292.50 - 51.63

240.87

The amount of pay after deductions was 240.87

Hope it helps and have an amazing day!

Answer:

$243.34425 round it up to the nearest 100th place

Step-by-step explanation:

9.75*30

=$295.5

=$295.5*10/100

for Federal income tax is $29.55

$295.5*6.2/100

Social Security tax $18.321 round it up $18/32

$295.5*1.45/100

Medicare tax is $4.28475 round it up to the nearest 100ths place $4.28

add all of them

$29.55+$18.321+4.28475= $52.15575 round it up = $52.16

sutract the amount you got paid

$295.5-$52.16=$243.34425

or you could have done

add all the %

10+6.2+1.45=17.65*295.5/100

=52.15575

hope it helped

Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

Answer:12:13

Step-by-step explanation:

it all comes down to one thing that is very good guessing and i so happen to have guess it right you welcome

Answer:

c

Step-by-step explanation:

im not for sure but i think its c

Answer:b

Step-by-step explanation:

The volume of a solid is found using the curve y = (1/9)x² and the line x=5.  And the volume is found to be 625π/18 cubic units.

A volume of a solid is used to determine how much space a particular object will take. It tells the amount of space that is present in an object. For example, if we consider a cylinder and fill it with water, the amount of water it can hold is the cylinder's volume.

Given the equation is y = (1/9)x² and x=5, y=0; about the y-axis. From the graph, the larger radius R = 5 and the smaller radius r=x=√(9y). Then, the limit is written as follows,

when x=0, y=0

when x= 5,  y = 1/9×(5)²=25/9

Now, the volume is calculated by using the integral as follows,

\(\begin{aligned}V&=\int^{25/9}_0 (\pi R^2-\pi r^2)\;dy\\&=\pi \int^{25/9}_0 ((5^2-(\sqrt{9y})^2)\;dy\\&=\pi \int^{25/9}_0 (25-9y)\;dy\\&=\pi\left[25y-\frac{9y^2}{2}\right]^{25/9}_{0}\\&=\pi\left[25\left(\frac{25}{9}-0\right)-\frac{9}{2}\left(\left(\frac{25}{9}\right)^2-0^2\right)\right]\\&=\pi \left[\frac{625}{9}-\frac{625}{18}\right]\\&=\frac{625 \pi}{18}\end{aligned}\)

The required answer is 625π/18 cubic units.

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The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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